A copper rod of length 086 m is lying on a frictionless tabl

A copper rod of length 0.86 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wore by an unstretched spring that has a spring constant of k = 88 N/m. A magnetic field with a strength of 0.26 T is oriented perpendicular to the surface of the table. What must be the direction of the current In the copper rod that causes the springs to stretch? If the current is 13 A, by how much does each spring stretch?

Solution

1.

since the magnetic field is oriented perpendicular to the table, the current flows from left to right from the right hand rule.

2.

the force is,

        F = kx + kx

   BiL = 2 kx

thus the stretched length is,

        x = BiL/2k

           = 0.26*13*0.86 / 2*88

           = 0.0165 m

           = 1.65 cm